A rectangular coil of area `5.0xx10^(-4) m^2` and 60 turns is pivoted about one of its vertical sides. The coil is in a radial horizontal field of 90 G (radial here means the field liners are in the plane of the coil for any rotation). What is the torsional constant of the hair spring connected to the coil if a current of 2.0 mA produces an angular deflection of `18^@`?

Explanation

To solve the problem step by step, we will use the relationship between the magnetic torque on the coil, the current flowing through it, and the torsional constant of the spring.

### Step 1: Identify the given values
- Area of the coil, \( A = 5.0 \times 10^{-4} \, \text{m}^2 \)
- Number of turns, \( N = 60 \)
- Magnetic field strength, \( B = 90 \, \text{G} = 90 \times 10^{-4} \, \text{T} \) (conversion from Gauss to Tesla)
- Current, \( I = 2.0 \, \text{mA} = 2.0 \times 10^{-3} \, \text{A} \)
- Angular deflection, \( \alpha = 18^\circ \)
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